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2 $Suppose revenue, R is predicted by the function Rlx) = (7x2 + 8)2 Determine the marginal revenue...

Question

2 $Suppose revenue, R is predicted by the function Rlx) = (7x2 + 8)2 Determine the marginal revenue

2 $ Suppose revenue, R is predicted by the function Rlx) = (7x2 + 8)2 Determine the marginal revenue



Answers

Find the marginal revenue for producing units. (The revenue is measured in dollars.) $$ R=-6 x^{3}+8 x^{2}+200 x $$

Let us have this problem right here, it's a differential equation. Okay, And let us do to 25 minus three X. Okay, So this is a separable differential equation. I can separate it once again, like we've been doing throughout some 7 10 tutorials before, so this is gonna be integral. And then this is gonna be our right. And this is gonna be to 25 X. And this is gonna be 3/2 X squared plus some arbitrary cost and see. Right? So this is a revenue. The revenue function. Okay, So this is an arbitrary constant and I want to take it away by finding a particular X. Right? So suppose I put X equals zero and I equated to zero. So this is gonna be zero equals 2 to 5 X zero X zero plus C. Right? So this is zero, this is zero and this is zero. So it means that C. Is equal to zero. So over here the sea is going to be zero. So then the revenue function finally is going to be 2 to 5 X minus three. Halfs X squared

For our kind of X equals 300 minus two X. We want to find our of X for R zero equals zero. So since our prime of X is purely a function of X. That is this a differential equation on the right hand side involves no other variables. We can simply solve by taking the anti derivative are primed to obtain are then we can plug in our initial conditions to solve this particular solution. So the anti derivative gifts are of X equals 300 X minus x squared plus C. We're seeing the cost of integration. We get from taking their anti derivative on indefinite integral. Thus we saw percy using our of zero equals zero. So are zero equals zero, gives 300 times zero minus zero squared plus C. Thus seeing is equal to zero plugging into our anti derivative. This gives us a final solution. R f x is equal to 300 x minus x squared.

Hey Guys Registry Probleble 13. In this problem, we need to find a marginal revenue function. And the revenue function is given, you know, the marginal living function is the derivative of the revenue function. Which we do know there's our prime X. And then we get the D. X. The first derivative of the revenue function here, which is four x minus 0.1 X square. We need to take the derivative of this equation and four is a constant. We can take it out then D. D X X. Then minus against 0.01 is a constant. Which we took out. Then the derivative. We need to take the derivative of X square from the power rule from the derivative rule. We know that when we take the derivative of extra depart end, we get in Multiplied Way Eggs to the War N -1. In this case the power is one. Therefore the derivative is one multiplied way extra power 1 -1. And here X is square. The derivative if we take we will get to multiplied by X. to the power to -1 because in his hair too. And then extradition one minus one gives us extra power zero and extra about two minus one. Here gives us Extra The Bar one. Then we have four multiplied by extra power zero and then -0.01 multiplied by 26. And anything to depart zero gives us one. Therefore four multiplied by one. We get four then minus 0.1, multiplied by 26 gives us 0102 and then we get our marginal function marginal revenue function Which is 4 -0.02 x.

64 via given the revenue function in terms of the units produced, we need to find a total revenue function and parties for the total revenue function. We gotta integrate both sides. This is the integration off our dash eggs. And here we have the integration of X squared minus one integration off X squares X Cuba with three using the power function minus integration of DX is just takes and then we have a constant of integration off. See, Now it has already given that are 00 So if we substitute that we have zero as zero plus c so concerned of integration of zero which we placed over here eso the final equation for the Rx. Consult us X cubed over tree minus X uh, and sees already zero. So that's it. Now, in part B, it asks us, but that why is it reasonable to produce? Are to substitute are 00 Why is this a reasonable assumption Are zero is equal to zero means X is equal to zero, which means that no unit has produced rather no unit has a soul on our is equal to zero means no revenue. So this is a quite reasonable because if we're not selling anything, how can we get any money? So if you can't get any money, it means that there is no revenue. That's why it is a reasonable assumption.


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